If two angles are supplementary the the same angle then they are congruent

Congruent Complements Theorem

If two angles are complementary to the same angle, then they are congruent

Vertical Angles Theorem

Vertical Angles are congruent

P13 Parallel Postulate || (point and line)

If there is a line and a point not on the line, then there is one line through the point parallel(||) to the given line

P14 Perpendicular Postulate ⊥ (point and line)

If there is a line and a point not on the line, then there is exactly one line through the point perpendicular(⊥) to the given line.

If two lines intersect to form a linear pair of congruent angles, then the lines are _____

If two lines intersect to form a linear pair of congruent angles, then the lines are PERPENDICULAR

If two sides of two adjacent acute angles are perpendicular, then the angles are _______

If two sides of two adjacent acute angles are perpendicular, then the angles are COMPLEMENTARY

If two lines are perpendicular, then they intersect to form four ______

If two lines are perpendicular, then they intersect to form four RIGHT ANGLES

P15 Corresponding Angles Postulate

If two parallel lines are cut by a transversal, then the pairs of corresponding angles are congruent

Alternate Interior Angles Theorem

If two parallel lines are cut by a transversal, then the pairs of alternate interior angles are congruent

Consecutive Interior Angles Theorem

If two parallel lines are cut by a transversal, then the pairs of consecutive interior angles are supplementary

Alternate Exterior Angles Theorem

If two parallel lines are cut by a transversal, then the pairs of alternate exterior angles are congruent

Perpendicular Transversal Theorem

If a transversal is perpendicular to one of two parallel lines, then it is perpendicular to the other

P16 Corresponding Angles Converse

If two lines are cut by a transversal so that the corresponding angles are congruent, then the lines are parallel

Alternate Interior Angles Thm Converse

If two lines are cut by a transversal so that alternate interior angles are congruent, then the lines are parallel

Consecutive Interior Angles Thm Converse

If two lines are cut by a transversal so that consecutive interior angles are supplementary, then the lines are parallel

Alternate Exterior Angles Thm Converse

If two lines are cut by a transversal so that alternate exterior angles are congruent, then the lines are parallel

If two lines are parallel to the same line, then they are ____ to each other

If two lines are parallel to the same line, then they are parallel to each other

In a plane, if two lines are perpendicular to the same line, then they are ______ to each other

In a plane, if two lines are perpendicular to the same line, then they are parallel to each other

P17 Slopes of Parallel Lines

Two lines are parallel if and only if they have the same slope (or are both vertical)

P18 Slopes of Perpendicular Lines

Two nonvertical lines are perpendicular if and only if the product of their slopes is -1 (negative reciprocals). Vertical and horizontal lines are perpendicular

Triangle Sum Theorem (& corollary for right angles)

The sum of the measures of the interior angles of a triangle is 180° | Corollary - the acute angles of a right triangle are complementary

Exterior Angle Theorem (for triangles)

The measure of an exterior angle of a triangle is equal to the sum of the measures of the two nonadjacent interior angles

Third Angles Theorem
(for triangles)

If two angles of one triangle are congruent to two angles of another triangle, then the third angles are also congruent. (180° - ∠A - ∠B) = ∠C

Properties of Congruent Triangles Theorem (three)

Reflexive: Every triangle is congruent to itself | Symmetric: if (∆ABC≅∆DEF) then (∆DEF≅∆ABC) | Transitive: if (∆ABC≅∆DEF and ∆DEF≅JKL) then (∆ABC≅∆JKL)

P19 SSS Congruence Postulate

If three sides of a triangle are congruent to three sides of a second triangle, then the two triangles are congruent

P20 SAS Congruence Postulate

If two sides and the included angle of one triangle are congruent to two angles and the included side of a second triangle, then the two triangles are congruent

P21 ASA Congruence Postulate

If two triangles and the included side of one triangle are congruent to two angles and the included side of a second triangle, the two triangles are congruent. (Also called ASAA or AAAS, can you see why?)

AAS Congruence Theorem

If two angles and the nonincluded side of one triangle are congruent to two angles and the corresponding nonincluded side of a second triangle, then the two triangles are congruent.
This can also be called AAAS or ASA, can you see why?